Thomas-Fermi model for quasi one-dimensional finite crystals

The model presented here applies a self-consistent method to electrons in crystals, thus enabling the calculation of the effective inner potential field. For this purpose, a Thomas-Fermi (TF) type model was developed, using a “qausi” one-dimensional finite crystal—a set of equidistant infinite thin plates representing the ionic planes, spread perpendicularly to a length axis. The model is applied to a finite crystal with no external fields. This application of a “multi-centered” TF model to an entire crystal is carried out for the first time in this work; the TF model was widely used in the past for atomic and molecular calculations, but in crystals it was limited to local use such as impurities. Poisson's (non-linear) differential equation describing the problem is solved using the highly efficient Relaxation Method. A pattern of almost periodical peaks (except near the boundaries) residing at the ionic sites is obtained for the potential, as well as for the electronic local density (indicating the electrons' tendency to pack mainly near the ions).